Rigidity of Conformally Compact Manifolds with the Round Sphere as the Conformal Infinity

Satyaki Dutta

Rigidity of Conformally Compact Manifolds with the Round Sphere as the Conformal Infinity

Differential Geometry 2008-01-08 v1

Authors: Satyaki Dutta

Abstract

In this paper we prove that under a lower bound on the Ricci curvature and an asymptotic assumption on the scalar curvature, a complete conformally compact manifold $(M^{n+1},g)$ , with a pole $p$ and with the conformal infinity in the conformal class of the round sphere, has to be the hyperbolic space.

Keywords

conformally compact manifolds rigidity Ricci curvature scalar curvature hyperbolic space conformal infinity

Cite

@article{arxiv.0801.0829,
  title  = {Rigidity of Conformally Compact Manifolds with the Round Sphere as the Conformal Infinity},
  author = {Satyaki Dutta},
  journal= {arXiv preprint arXiv:0801.0829},
  year   = {2008}
}

Comments

23 pages

Related papers

View all related →